Old news. This ranks up there with the fact that it was a bad idea to use base 10 instead of base 12. Absolutely and utterly true, but completely not worth the switching costs.
Well, it’s certainly too hard to practically switch, and so we won’t. But that doesn’t necessarily mean it’s not worth the cost. We’ve apparently had π in its current form for for 300 years; we’re going to have to live with it much longer than that.
The way to actually make a change like that though, assuming we wanted to, would be to just make up a new symbol for 2π, and start using it. For a while, the two symbols would coexist, and then someday the π symbol would just start to fade out.
(Probably about as easy to change in practice as switching to metric dates and times, as the French tried to do after the revolution.)
I remember the moment as a kid when I realized that the number 10 wasn't some magical number, but just some arbitrary number we've decided to use as a base. Definitely a stupid choice IMHO, but it's what we're stuck with.
Base 10 may not be completely arbitrary, but is is undoubtedly lazy.
It would have actually been more useful to use 8 fingers = octal.
But then who counts with their fingers these days?
(2^10 - 1 : you have 10 digits on your hands. This also assumes you have a value for 0.)
Sadly, I know this from experience.
However, if you bother thinking about the word arbitrary too hard (as your comment inspired me to do), you end up in the realm of existentialism and down the proverbial rabbit hole.
For instance if we assume that half the time we need to divide into halves, 1/4 of the time into thirds, 1/8 into quarters and so on, then over 90% of the time you wish to split something into 1/2, 1/3, 1/4, 1/6 or 1/12. All of which are trivial in a duodecimal system. By contrast only 56% of the time do you wish to split into the similarly easy 1/2, 1/5 or 1/10 in decimal. Even if we say that 1/4 and 1/8 are OK in decimal, we still wind up with inconvenient repeating fractions over 3 times as often as duodecimals do.
However, I was impressed by the far-reaching implications of this fact. The regularity of the base 12 times table was particularly compelling. You know how easy the 2's and 5's row is to learn on the times table, right? There's an obvious pattern that's easy to memorize? Lots of numbers are like that in base 12.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...
But it seems unlikely as the origin of the Babylonian system cited. The 60 symbols are written in base 10; if it grew out of a culture that counted to twelve on their fingers, I'd expect to see five groups of twelve, not six groups of ten.
I can think of a more natural explanation. When I am counting something on my fingers (in the conventional way), I often want a way to store the tens digit. Perhaps the Babylonians did, too. That the tens digit is drawn as two groups of three is suggestive that whatever method they used stored a trinary and a binary state.
So, when I count off (palms up), I get to ten on the thumb of my right hand. It has a little more dexterity than my other fingers and can store more states. It's pretty straightforward to get to six by leaving it bent/straight and pointing out/up/in. It's natural to do while counting, too. (Bent and pointing in is a little uncomfortable if I want to use the other fingers, but then . . . you don't ever need to actually store 'six').